By J. S. Fitzgerald (auth.), Martin Wirsing, Maurice Nivat (eds.)

ISBN-10: 354061463X

ISBN-13: 9783540614630

This publication constitutes the refereed complaints of the fifth foreign convention on Algebraic method and software program know-how, AMAST '96, held in Munich, Germany, in July 1996.
The booklet offers 25 revised complete papers chosen from a complete of sixty seven submissions and 23 approach demonstrations; additionally integrated are six invited talks and 6 invited shows of the AMAST schooling Day on commercial purposes of formal tools. the whole papers are geared up in topical sections on theorem proving, algebraic specification, concurrent and reactive platforms, application verification, common sense programming and time period rewriting, and algebraic and logical foundations.

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Extra info for Algebraic Methodology and Software Technology: 5th International Conference, AMAST '96 Munich, Germany, July 1–5, 1996 Proceedings

Sample text

An intuitive definition of k-degenerate graphs is as follows: G is k-degenerate if there exists a vertex v of G with vertex degree less than or equal to k such that G \ {v} has the same property. More formally, a graph G is k-degenerate if vertices V can be ordered (v1 , v2 , · · · , vn ) such that degGi (vi ) ≤ k, where Gi is the subgraph of G induced by the vertices {vi , vi+1 , · · · , vn }. For example, trees are 1-degenerate as there exists a leaf of vertex degree 1 and after deleting it the graph is still a tree.

In each move one guard is moved from it current position (vertex) to a new position. D(i) denotes the set of vertices where the guards are placed after i moves. Formally, the search is a sequence of k-sets: D(0), D(1), . . , D(M ), where D(i−1)∩D(i) is denoted by S(i) and has cardinality k − 1 for all i > 0. A vertex is said to clear if it was in the neighborhood of some guard in some previous move and since then no path has been established between this vertex and a contaminated (fugitive may potentially be on it) vertex without passing through the neighborhood of a guard in the current position.

S(i) ∈ / L for all 1 ≤ i ≤ M . Proof. Assume S(i) ∈ L. If Ud (i) was equal to V then there would have been no need for the i-th move. So there is at least one contaminated vertex just before this move. During this move there is only one guard on the graph, at S(i). Since the induced graph on V − N [S(i)] is connected, entire set V − N [S(i)] will get contaminated. So the set of clear vertices after this move will be N [p1 (i)] ∪ N [p2 (i)]. This state can be achieved at the start of the search by placing the guards at p1 (i) and p2 (i).

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Algebraic Methodology and Software Technology: 5th International Conference, AMAST '96 Munich, Germany, July 1–5, 1996 Proceedings by J. S. Fitzgerald (auth.), Martin Wirsing, Maurice Nivat (eds.)

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